Forces

Range of Possible Resultants

Finding the Maximum and Minimum Resultant of Two Forces

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Do Now warm-up prompt

A boy and his sister exert a 5 N force eastward on a dresser. If their mother wants to prevent them from moving the dresser, how large must her force be?

Angles and Resultants

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Video Instruction

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C. Combining Forces

Range of Possible Resultants

Case III

θ ≠ 0° ≠ 180°

Given

Forces of 100. N and 30. N act on a body.
Find: Largest Possible Resultant.
Find: Smallest Possible Resultant.

↓

Largest Possible Resultant = 100. N + 30. N

= 130 N

Smallest Possible Resultant = 100. N − 30. N

= 70. N

Subtract the two forces to find the Smallest Resultant

Add the two forces to find the Largest Resultant

Concurrent Forces

All forces pass through a common point

Example 1

Concurrent forces diagram, example 1 Resultant construction for example 1

Example 2

Concurrent forces diagram, example 2 Resultant construction for example 2
Concurrent forces, example 3

Not Concurrent

Forces that are not concurrent
Given

Which pair of concurrent forces may have a resultant of 20 nt?
a) 5 nt + 10 nt
b) 20 nt + 20 nt
c) 20 nt + 50 nt
d) 30 nt + 5 nt

Hint: Find the range of possible resultants for each choice

↓
ChoiceMaxMin
a) 5 nt + 10 nt15 nt5 nt
b) 20 nt + 20 nt40 nt0 nt
c) 20 nt + 50 nt70 nt30 nt
d) 30 nt + 5 nt35 nt25 nt

Check Your Understanding

5 quick questions — pick an answer to see if you’re right.

1. Forces of 100. N and 30. N act on a body. What is the largest possible resultant?

2. Forces of 100. N and 30. N act on a body. What is the smallest possible resultant?

3. Which pair of concurrent forces could have a resultant of 20 N?

4. What are concurrent forces?

5. A boy and his sister each push a dresser 5 N east. What force must their mother apply to keep it from moving?

NYSSLS Regents Practice · Forces · Patterns & Limits

Two Tugboats and a Barge

Two tugboats push a barge. Tugboat 1 exerts 3000. N and tugboat 2 exerts 4000. N. The captains can change the angle between the two forces from 0° (same direction) to 180° (opposite directions).

Which resultant force is not possible for these two tugboats?

▶ Want a challenge? Open 6 more Regents-style questions  (harder · mixed formats)

Challenge score: 0 / 6

Substitute values

C1. The captains aim the tugboats at 90° to each other. Substitute numerical values into a mathematical representation that can be used to determine the magnitude of the resultant force on the barge. Then calculate the resultant.

R = √(F12 + F22) = √((F1 = N)2 + (F2 = N)2) = N
Multiple choice

C2. At what angle between the forces is the resultant greatest, and what is its magnitude?

Select all that apply

C3. Place a check mark in three boxes to indicate resultant forces that the two tugboats could produce on the barge.

Support or Refute · Justify

C4. A student makes the following claim.

Claim: No matter how the captains aim the two tugboats, the resultant force on the barge can never be less than 1000. N.

Place a check mark in either the Support or Refute box. Justify your response using a mathematical relationship.

Multiple choice

C5. Which graph best represents the magnitude of the resultant as the angle between the forces increases from 0° to 180°?

Constructed response

C6. To steer the barge into a narrow dock, the captains plan to push at 90° to each other instead of in the same direction. Identify one benefit and one drawback of this plan.

Resultants at Other Angles →